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Combined analysis of Planck and SPTPol data favors the early dark energy models

Anton Chudaykin, Dmitry Gorbunov, Nikita Nedelko

TL;DR

This work probes the consistency of Planck and SPTPol CMB measurements within $\Lambda$CDM by restricting Planck to $\ell<1000$ and incorporating SPTPol polarization and lensing data, which yields robust cosmological parameter constraints and reduces the $S_8$ tension with large-scale structure probes. It then tests Early Dark Energy (EDE) as a pre-recombination energy injection, modeling both background and perturbations for a scalar field with $V_n(\phi)=V_0\,\frac{\phi^{2n}}{2^n}$ and finding that, for $n=3$, EDE can raise $H_0$ to $\approx73$ km s$^{-1}$Mpc$^{-1}$ while keeping $S_8$ compatible with lensing constraints; adding BAO and SN data yields further consistency with the drag-scale $r_{\rm drag}$ and strengthens the case for EDE with a nonzero $f_e$. Allowing $n$ to vary does not improve the fit beyond $n\approx2.5$–$3$, indicating robustness of the EDE interpretation. Overall, the combined data approach reduces the Hubble tension to about $2.5\sigma$ in $\Lambda$CDM and shows that EDE can alleviate this tension without degrading large-scale structure constraints, with a significant improvement in goodness-of-fit relative to standard $\Lambda$CDM. The results underscore the potential of early-Universe modifications to resolve current cosmological tensions and guide future surveys such as DESI, Euclid, and LSST.

Abstract

We study the implications of the Planck temperature power spectrum at low multipoles, $\ell<1000$, and SPTPol data. We show that this combination predicts consistent lensing-induced smoothing of acoustic peaks within $Λ$CDM cosmology and yields the robust predictions of the cosmological parameters. Combining only the Planck large-scale temperature data and the SPTPol polarization and lensing measurements within $Λ$CDM model we found substantially lower values of linear matter density perturbation $σ_8$ which bring the late-time parameter $S_8=σ_8\sqrt{Ω_m/0.3}=0.763\pm0.022$ into accordance with galaxy clustering and weak lensing measurements. It also raises up the Hubble constant $H_0=69.68\pm1.00{\rm \,\,km\,s^{-1}Mpc^{-1}}$ that reduces the Hubble tension to the $2.5σ$ level. We examine the residual tension in the Early Dark Energy (EDE) model which produces the brief energy injection prior to recombination. We implement both the background and perturbation evolutions of the scalar field which potential scales as $V(φ)\propto φ^{2n}$. Including cosmic shear measurements (KiDS, VIKING-450, DES) and local distance-ladder data (SH0ES) to the combined fit we found that EDE completely alleviates the Hubble tension while not degradating the fit to large-scale structure data. The EDE scenario significantly improves the goodness-of-fit by $2.9σ$ in comparison with the concordance $Λ$CDM model. The account for the intermediate-redshift data (the supernova dataset and baryon acoustic oscillation data) fits perfectly to our parameter predictions and indicates the preference of EDE over $Λ$CDM at $3σ$.

Combined analysis of Planck and SPTPol data favors the early dark energy models

TL;DR

This work probes the consistency of Planck and SPTPol CMB measurements within CDM by restricting Planck to and incorporating SPTPol polarization and lensing data, which yields robust cosmological parameter constraints and reduces the tension with large-scale structure probes. It then tests Early Dark Energy (EDE) as a pre-recombination energy injection, modeling both background and perturbations for a scalar field with and finding that, for , EDE can raise to km sMpc while keeping compatible with lensing constraints; adding BAO and SN data yields further consistency with the drag-scale and strengthens the case for EDE with a nonzero . Allowing to vary does not improve the fit beyond –, indicating robustness of the EDE interpretation. Overall, the combined data approach reduces the Hubble tension to about in CDM and shows that EDE can alleviate this tension without degrading large-scale structure constraints, with a significant improvement in goodness-of-fit relative to standard CDM. The results underscore the potential of early-Universe modifications to resolve current cosmological tensions and guide future surveys such as DESI, Euclid, and LSST.

Abstract

We study the implications of the Planck temperature power spectrum at low multipoles, , and SPTPol data. We show that this combination predicts consistent lensing-induced smoothing of acoustic peaks within CDM cosmology and yields the robust predictions of the cosmological parameters. Combining only the Planck large-scale temperature data and the SPTPol polarization and lensing measurements within CDM model we found substantially lower values of linear matter density perturbation which bring the late-time parameter into accordance with galaxy clustering and weak lensing measurements. It also raises up the Hubble constant that reduces the Hubble tension to the level. We examine the residual tension in the Early Dark Energy (EDE) model which produces the brief energy injection prior to recombination. We implement both the background and perturbation evolutions of the scalar field which potential scales as . Including cosmic shear measurements (KiDS, VIKING-450, DES) and local distance-ladder data (SH0ES) to the combined fit we found that EDE completely alleviates the Hubble tension while not degradating the fit to large-scale structure data. The EDE scenario significantly improves the goodness-of-fit by in comparison with the concordance CDM model. The account for the intermediate-redshift data (the supernova dataset and baryon acoustic oscillation data) fits perfectly to our parameter predictions and indicates the preference of EDE over CDM at .

Paper Structure

This paper contains 13 sections, 12 equations, 6 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Data sets and numerical procedure
  3. Cosmological data
  4. Numerical procedure
  5. Methodology and $\Lambda$CDM constraints
  6. $A_L$ test
  7. Early Dark Energy model
  8. Background dynamics
  9. Perturbed dynamics
  10. Cosmological constraints within the Early Dark Energy model
  11. Parameter constraints for $n=3$
  12. Promoting $n$ to a free parameter
  13. Conclusion

Figures (6)

  • Figure 1: Marginalized parameter constraints for the $\Lambda$CDM model using different datasets. We explore independently $\rm PlanckTT\text{-}low\ell$ and $\rm SPTPol$, combined likelihood $\rm PlanckTT\text{-}low\ell\!+\!SPTPol$ along with SPTPol lensing, $\rm PlanckTT\text{-}low\ell\!+\!SPTPol\!+\!Lens$. For comparison we include constraints from the baseline Planck analysis $\rm PlanckTTTEEE$ as well. The gray bands represent the $1\sigma$ and $2\sigma$ constraints on $S_8$ and $H_0$ coming from Joudaki:2019pmv and Riess:2019cxk.
  • Figure 2: Left panel: evolution of the energy density of the scalar field relative to total energy density of the universe for several values of $n$\ref{['V']}. Right panel: The scalar field equation of state, the adiabatic sound speed $c_a^2$ and the effective sound speed $c_s^2$ for various $k$ as a functions of scale factor. Both panels: evolution of all quantities is obtained with $f_e=0.1$, $z_c=3000$. The vertical dashed black line refers to $z_c=3000$.
  • Figure 3: Left panel: the evolution of the density contrast of the scalar field for a set of momentum $k$. Right panel: the evolution of the heat-flux for a set of $k$. Both panels: the evolution of the quantities is obtained for $f_e=0.1$, $z_c=3000$. The vertical dashed black line refers to $z_c=3000$.
  • Figure 4: Marginalized parameter constraints for the $\Lambda$CDM and EDE models using various datasets. We explore the parameter space using the $\rm Base\!+\!S_8\!+\!H_0$ dataset with and without intermediate redshift probe $\rm BAO\!+\!SN$. For comparison we include constraints from the Base data set only in $\Lambda$CDM model. The Base dataset includes $\rm \!PlanckTT\text{-}low\ell\!+\!SPTPol\!+\!Lens$. The gray bands represent the $1\sigma$ and $2\sigma$ constraints on $S_8$ and $H_0$ coming from Joudaki:2019pmv and Riess:2019cxk.
  • Figure 5: The marginalized posterior distribution in the plane $(S_8,\,H_0)$ for two data set combinations $\rm Base\!+\!S_8\!+\!H_0$ ( left panel) and $\rm Base\!+\!S_8\!+\!H_0\!+\!BAO\!+\!SN$ ( right panel) in the $\Lambda$CDM and EDE models. The scattered points represent values of $f_e$. The gray bands represent the $1\sigma$ and $2\sigma$ constraints on $S_8$ and $H_0$ coming from Joudaki:2019pmv and Riess:2019cxk. The Base dataset includes $\rm \!PlanckTT\text{-}low\ell\!+\!SPTPol\!+\!Lens$.
  • ...and 1 more figures